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Open Access Publications from the University of California

Limit cycles in four dimensions

  • Author(s): Fortin, JF
  • Grinstein, B
  • Stergiou, A
  • et al.

We present an example of a limit cycle, i.e., a recurrent flow-line of the beta-function vector field, in a unitary four-dimensional gauge theory. We thus prove that beta functions of four-dimensional gauge theories do not produce gradient flows. The limit cycle is established in perturbation theory with a three-loop calculation which we describe in detail. © 2012 SISSA, Trieste, Italy.

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